Volume of a Solid (Washer method) Example.

 

How to use a TI-84 to find the volume of a hollow solid (which is ofter referred to "the washer" method since our circular cross-sections will have a hole in them.  Others prefer the name "annular disk" or "ring"

SFHS students can follow this link: https://www.deltamath.com/app/assignment/15468561

Everyone can download a pdf at mathorama.com

Inverse Functions Have Reciprocal Slopes (5.R p 400 #39)

 Inverse Functions Have Reciprocal Slopes (5.R p 400 #39)

Elliptical Orbit in a Polar Form (10.6 p745 #59)

 

Elliptical Orbit in a Polar Form (10.6 p745 #59)  

Not only do we answer the question at hand, we derive the polar form of a conic section.

If you want to skip ahead: 

Minute 5:45 Finding the distance between the surface of Earth and Explorer 18 when the angle is 60 degrees

Minute 12:53 Proof that e = c/a = 2c/2a=(distance between focii/major axis) 

Derivatives of Inverse Functions on the TI-84 (5.3 p 340 #71)

 Derivatives of Inverse Functions on the TI-84 (5.3 p 340 #71)

Review of a Midpoint Riemann Sum (5.2 p 331 #77)

 Review of a Midpoint Riemann Sum (5.2 p 331 #77)

Another Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)

 Another  Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)

Slope Fields and Differential Equations with Natural Logs (5-2 p330 #49)

 Slope Fields and Differential Equations with Natural Logs (5-2 p330 #49)

A slope field and a diffyQ checked with the TI-84

A Tangent Line Confirmed with the TI-84 (5-1 p322 #69)

 A Tangent Line Confirmed with the TI-84 (5-1 p322 #69)

We confirm our result with the (DRAW)(5:Tangent) feature on the TI-84

Basic Use of the First Fundamental Theorem (4-R p 310 #41)

 Basic Use of the First Fundamental Theorem (4-R p 310 #41)

Here we use the First Fundamental Theorem of Calculus to evaluate a definite integral, and we will check our work with a TI-84 calculator,

Riemann Sums to Estimate an Integral (4-R p 309 #25)

 Riemann Sums to Estimate an Integral (4-R p 309 #25)

Here we use left and right Riemann sums to get the upeer and lower bounds on an integral. We can then use the TI-84 to check our work.

Mean Value Theorem for Integrals with the TI-84 (4-5#85)

Mean Value Theorem for Integrals with the TI-84 (4-5#85)

Estimating Average Sales with t he TI-84 and the Mean Value Theorem for Integrals (4-5#85)

Is the Alternating Series Remainder Theorem Not Working?

 

This appears to be a counter example that would disprove the Alternating Series Remainder Theorem.... 

Estimating a Definite Integral (4.3 p278 #53)

 

Estimating a Definite Integral (4.3 p278 #53)

Estimating a definite integral with the area of rectangles. 

Review of Sigma Sums (4.2 p 267 #9, 22)

 Review of Sigma Sums (4.2 p 267 #9, 22)

We explain some useful sum formulas, work some examples, then show how to use the TI-84 to confirm our result.

How High Will It Go (in Europe) (4.1 p. 256) # 60

 

How High Will It Go (in Europe) (4.1 p. 256) # 60

This time we find the maximum height of a ball thrown into the air in meters.  All we need to know is the velocity and height when it is thrown! In this one we use the constant acceleration of 9.8 meter per second per second.

Minimizing Length (3.7 (p 225) #23)

Minimizing Length (3.7 (p 225) #23)

Here we use a calculator to find the minimum length of a line that goes through a point.  This is actually a great method for figuring out the length of something going around a corner, like we will demonstrate in a later video

 

TI-84 Tips to Show Curves are Orthogonal To Each Other (2.5 #63)

 TI-84 Tips to Show Curves are Orthogonal To Each Other (2.5 #63)

Here we use a TI-84 to show how two curves are orthogonal to each other.  If they are, then the tangent lines's slope at the points of intersection are perpendicular, and be negative reciprocals of each other:

If the slope is a/b, then the perpendicular slope is -b/a.  The calculator has a (CALC)5. intersect feature and a (CALC)6. dy/dx feature, so this is how we can tell if the curves are orthogonal.